On the diamond operator related to the wave equation
In this paper, we study the solution of the equation ◇ku(x) = f (x) where ◇k is the Diamond operator iterated k times and is defined by ◇k ((∑i=1p ∂2/∂xi2)2 -(∑j=p+1p+q ∂2/∂xj2)2)k where p+q = n is the dimension of the n-dimensional Euclidean space Rn, x = (x1, x2, ..., xn) ∈ Rn, k is a nonnegative...
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| Format: | Article |
| Language: | English |
| Published: |
2014
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| Online Access: | http://www.scopus.com/inward/record.url?eid=2-s2.0-0035425986&partnerID=40&md5=1e02c1a1882767e2eb169871cbb334f2 http://cmuir.cmu.ac.th/handle/6653943832/4792 |
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| Institution: | Chiang Mai University |
| Language: | English |
| Summary: | In this paper, we study the solution of the equation ◇ku(x) = f (x) where ◇k is the Diamond operator iterated k times and is defined by ◇k ((∑i=1p ∂2/∂xi2)2 -(∑j=p+1p+q ∂2/∂xj2)2)k where p+q = n is the dimension of the n-dimensional Euclidean space Rn, x = (x1, x2, ..., xn) ∈ Rn, k is a nonnegative integer, u(x) is an unknown and f is a generalized function. It is found that the solution u(x) depends on the conditions of p and q and moreover such a solution is related to the solution of the Laplace equation and the wave equation. |
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